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MATHEMATICA GUIDE
Rules & Patterns
At the core of Mathematica's symbolic programming paradigm is the concept of transformation rules for arbitrary symbolic patterns. Mathematica's pattern language conveniently describes a very general set of classes of expressions, making possible uniquely readable, elegant and efficient programs.
Featured Examples |
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Define a Function for Repeated Expressions
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Dynamically Adjust the Parameters of a Differential Equation
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Get the Number of Points Used to Plot a Curve
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Implement the Bubble Sort Algorithm with Patterns and Rules
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Implement the Heap Sort Algorithm with Patterns and Rules
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Include Delay Differential Equations Directly in Dynamic Simulations
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Remove Tags from Imported HTML
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Successively Replace Entries in an Array
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Use Rules Iteratively
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Verify the Solution to an Equation
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Visualize Solutions to Equations
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Visualize the Lorenz Attractor
Reference
Rules »
lhs→rhs (Rule) — representation of replacement rule
expr/.rules (ReplaceAll) — apply replacement rules to an expression
RuleDelayed(:>) ▪ ReplaceRepeated(//.) ▪ Condition(/;) ▪ ...
Patterns »
x_ — any expression, named 
x__ — sequence of expressions
a|b|c — alternative forms
Repeated(..) ▪ Except ▪ Longest ▪ Shortest ▪ ...
Pattern Matching Functions »
Cases — elements of a list or expression matching a given pattern
Position ▪ MemberQ ▪ MatchQ ▪ Count ▪ DeleteCases ▪ ...
